Antenna arrays having phase and amplitude control

ABSTRACT

THIS INVENTION PROVIDES IMPROVED ANTENNA ARRAYS HAVING CHARACTERISTICS THAT ARE MATCHED WITH THE GEOMETRIC CONFIGURATION OF THE ELECTROMAGNETIC WAVES THAT ARE TO BE RADIATED (I.E. TRANSMITTED FORM OR RECEIVED) BY THE ARRAY, FOR OPTIMAL PERFORMANCE. SUCH ARRAYS HAVE A GREATLY INCREASE ANGULAR RANGE OF DIRECTIVITY. ACCORDING TO THE INVENTION, THE SPACING OF THE INDICIDUAL RADIATORS OF THE ARRAY, THE FIELD-STRENGTH-DISTRIBUTION PATTERN OF THE ENERGY FED TO OR FROM THE INDIVIDUAL RADIATORS, AND THE PHASE-DISTRIBUTION PATTERN OF SAID FEED ENERGY ACROSS THE ARRAY ARE SO PREDETERMINED AND CORRELATED THAT THE BEHAVIOR OF THE ARRAY AS A WHOLE IS MADE TO BE SUBSTANTIALLY IDENTICAL WITH THAT OF AN IMAGINARY, COHERENTLY RADIATING APERTURE HAVING THE SAME OVERALL CONFIGURATION AS THE ARRAY, IN RESPECT TO WAVES OF THE PRESCRIBED GEOMETRIC CONFIGURATION.

' vs. v. DRABOWITCH $553,692 ANTENNA ARRAY HAVING PHASE ANDAMPLITUDE-CONTROL Filed Get. 5. 1966 2 Sheets-Sheet 1 T 2 :{NVENTORSerge mrabawzich Attorney J 1971 s. v. DRABOWITCH 53,

Filed Oct. 5, 1966 ANTENNA ARRAYS HAVING PHASE AND AMPLITUDE CONTROL 2Sheets-Sheet 2 INVENTOR e rg e V. Drabowifch Attorney United StatesPatent 2 rm. (:1. I-l01g 13/00 US. Cl. 343778 Claims ABSTRACT OF THEDISCLOSURE This invention provides improved antenna arrays havingcharacteristics that are matched with the geometric configuration of theelectromagnetic waves that are to be radiated (i.e. transmitted from orreceived) by the array, for optimal performance. Such arrays have agreatly increased angular range of directivity. According to theinvention, the spacing of the individual radiators of the array, thefield-strength-distribution pattern of the energy fed to or from theindividual radiators, and the phase-distribution pattern of said feedenergy across the array are so predetermined and correlated that thebehavior of the array as a whole is made to be substantially identicalwith that of an imaginary, coherently radiating aperture having the sameoverall configuration as the array, in respect to waves of theprescribed geometric configuration.

BACKGROUND In the art of antenna construction, it is known to provideantenna arrays consisting of a plurality of individual, elementaryantennas or radiators spaced along a predetermined direction to providea linear array, or along each of two coordinate directions to provide atwo-dimensional or surface array. Such arrays have made it possible toachieve desired directional diagrams and radiate waves having prescribedgeometric configurations, for example, plane waves propagating in aprescribed direction, or spherical waves centered at a prescribed focusor source point.

In arrays of this type, it is known to feed energy to and from theindividual radiators by way of phase shifters, and so to adjust thephase shifters that the phase distribution of the electromagnetic energyacross the array is made to be approximately the same as that of acoherent wave having a prescribed configuration. Thus, it is obvious forexample that if all the phase shifters are adjusted in like manner, thenthe array will radiate a plane wave propagating in a direction normal tothe array. Suitable difierential adjustment of the phase shifts makes itpossible to simulate in an approximate manner coherent waves having anyof various prescribed geometric characteristics.

For example, my co-pending application Ser. No. 583,552 of even datediscloses antenna arrays of the type just indicated, which constitutesecondary focusing lens assemblies and are associated with severalprimary antenna sources, so as to convert spherical waves radiated by aselected primary source into plane waves propagating in a controllabledirection of space, and vice versa. The said copending application alsodisclosed digital electronic means for sequentially controlling theadjustment of the phase shifters of the array so as to accomplish whatmay be termed electronic scanning operation for radar and relatedapplications.

Radiator arrays of the general class described above ice have manyimportant advantages including flexibility and simplicity, and arecurrently gaining wide acceptance in advanced radar and communicationsystems. However, theoretical and practical experience has revealed thatsuch arrays as heretofore constructed suffer from certain seriousdefects. Thus, in the important cases where the arrays have been usedfor electronically controlled scanning, it has not been possible toachieve simultaneously large scanning angles and elimination ofhigh-amplitude sidelobes while maintaining a sufficiently great spacingbetween the radiators of the array to avoid spurious coupling betweenthem. To prevent the formation of such sidelobes, it was necessaryinstead to bring the radiators nearer to each other and thus tolerate arelatively high intercoupling or to limit the angular scanning range, orelse to be content with a rather unsatisfactory compromise between thethree factors: sidelobes, angular scanning, coupling. Also, spuriouscoupling between adjacent radiators of the array has introduceduncontrollable variations in the gain and the radiation pattern of theantenna system during scanning operations. The presence of thesidelobes, which limit the scanning angles, is due to the essentiallydiscontinuous character of the array which permits the control of thephase of the radiated wave but at regularly equispaced points. Thesedefects have seriously limited the usefulness of the radiator arrays ofthe kind to which the invention relates.

DESCRIPTION OF THE INVENTION It is the general object of this inventionto eliminate the above-noted and similar deficiencies of conventionalradiator arrays in an almost complete way, and thereby greatly toimprove the operating characteristics and extend the usefulness of sucharrays.

According to the invention, it has been found that despite theessentially discontinuous character of the array, a consequence of thefinite number of individual radiators of which it is composed,the'behavior of the array in respect to waves of a prescribed geometricconfiguration can be made to simulate remarkably closely the theoreticalbehavior with reference to such waves of a fictive continuous radiantsource or aperture having the same overall shape as the array. Thisresult is reached by apply ing certain definite teachings, to bepresently set forth, to the structural and operating parameters of theradiators of the any, so as to correlate those parameters with thespecific geometric configuration of the waves to be radiated by thearray. When such correlation has been achieved and the theoreticalcharacteristics of a continuous radiant source have thereby beensimulated, it is found that the operation of the array has beenoptimized in respect to the prescribed Wave configuration. Thepreviously observed deficiencies are virtually completely eliminated.Inter-radiator coupling is reduced practically to zero. Both thedirectional characteristic and the scanning range to the array can besimultaneously maximized, so long as the particular wave geometry forwhich the array was constructed is maintained.

Specific embodiments of the invention will now be described, forillustrative purposes and without limitative intent, with reference tothe accompanying drawing, wherein:

FIG. 1 schematically illustrates a simple linear array as used in asystem according to the invention for radiating plane waves ofprescribed direction over a wide scanning range;

FIG. 2 illustrates part of the improved array in somewhat greaterdetail, together with the associated fieldstrength-distribution patternused according to the invention;

FIG. 3 shows a preferred consruction of an array according to theinvention, using paired multimode radiators;

FIG. 4 is a curve illustrating a typical array factor; and

FIG. 5 schematically illustrates the geometry of an array according tothe invention when used in association with a primary source radiatingspherical waves.

In the present specification and claims, the word radiate and itsderivatives are to be construed with their broad meaning usual inantenna engineering, as applying to both the transmission and thereception of electromagnetic wave energy. Thus, an elementary antenna orradiator is said to be radiating energy not only when it is operating toemit as waves propagating in space electromagnetic energy fed to it, butlikewise when it is picking up or absorbing space waves and transferringthe energy picked up therefrom to a receiver connected by a feederjunction to said radiator. In a corresponding manner, the word feed andits derivatives serves to describe the transfer of electromagneticenergy by way of a conductor or waveguide both to and from a radiator.

Shown in FIG. 1 is a linear array comprising a series of radiatorelements aligned on an axis OX and numbered l, 2, n. The elements areshown at a uniform spacing designated a. The total width of the array isd=na. The midpoint of the array is I and the normal to O-X at I is I-Z.An array of the kind shown may be used to radiate waves of variousgeometric configurations. For example, it may be desired to cause thearray to radiate plane parallel waves in a prescribed direction of spacedefined by a specified angle 0a with respect to the normal I-Z, all theplane waves being normal to such prescribed direction. This requirementarises, in particular, when the array is to be used as a directionaltransmitting and/ or receiving antenna system for transmitting radioenergy e.g. in the form of radar pulses towards a target, and forreceiving echo pulses from the target.

The normal way of controlling the space configuration of the wavesradiated by an array is to control the phase distribution of the waveenergy fed to (or from) the individual radiators of the array. If allthe radiators are fed in parallel from a common signal source withoutany mutual phase displacement between the signals applied to therespective radiators, it is evident that the radiator array will radiatea planar wave propagating in the normal direction I-Z. If equal phaseshifts are introduced between the signals applied to adjacent radiatorsof the array, the wave radiated from the array will still be planar, butwill propagate in a direction inclined to the normal in one or the othersense, depending on the sign of the phase shift, by an angle acorresponding to the phase shift angle. Similarly, the distributionpattern of phase-shifts between the signals fed to (or from) therespective radiators of an array can be modified so as to cause thearray to radiate spherical waves focused on a prescribed focal point orcenter, as disclosed in my co-pending application identified above andas later described. Other geo metric configurations of radiated wavescan similarly be obtained by controlling the phase-distribution patternsof energy fed to or from the array.

Thus the phase distribution between the radiators of the array is usedto control the main directional lobe of the over-all radiation patternof the array. By controlling the phase distribution (for instance by thedigital phaseshift-control means described in my said co-pendingapplication), the angular position of the main lobe of the over-allradiation pattern can be varied, as for scanning purposes. This type ofscanning is sometimes termed electronic scanning in contrast to the moreconventional mechanical scanning which involves mechanically displacingan antenna.

Conventional electronic scanning, and more broadly the conventionalcontrol of the spatial configuration of the waves radiated by an arrayby acting on the phase distribution of the signals fed to and from therespective radiators of the array, has been found deficient in manyrespects. The radiating elements heretofore used in such arrays havegenerally been omnidirectional in character, arranged at a spacinggreater than half the operating wavelength. With such an array, theover-all radiation pattern has a central or main lobe and a pair ofsecondary lobes substantially symmetrically positioned on opposite sidesof the main lobe. For large deviation angles of the main lobe of thearray, e.g. for antenna scanning angles approaching one of the secondarylobes increases inordinately in field strength, so as to becomecomparable to the main or central lobe. The directional characteristicsof the system are then seriously disturbed; for example, spurious targetechoes are introduced into a radar system. To obviate this, thedeflection angles, i.e. the scanning range, have had to be drasticallylimited.

If directional sources, rather than omnidirectional ones, are used asthe elementary radiators of the array, then the width of the main lobeof each radiator again sets a definite limit to the maximum scanningangle achievable without excessively reducing the gain of the array.

Another defect of such conventional radiator arrays is thatobjectionable interaction or coupling occurs between adjacent radiatorsof the array, producing differential variations in the elementaryradiation patterns of the radiators as the deflection angle (or scanningdirection) is varied, with corresponding uncontrollable variations inantenna gain over the scanning range.

The present invention is based on the finding that the above andanalogous deficiencies of conventional radiator arrays and electronicscanning systems using the same can be effectively eliminated if thefield-distribution pattern, in respect to both amplitude and phase, ofthe energy fed to or from the individual radiators and theinter-radiator spacing are correlated, in accordance with certaindefinite teachings, with the spatial configuration of the waves that areto be radiated by the array.

This invention represents a development in the application of signaltheory to antenna design and construction. The theoretical principles ofthe application of signal theory to radio antennas have been publishedpreviously by me in LOnde Electrique, May 1965, page 550 et seq., in anarticle entitled Application de la Thorie du Signal aux Antennes. Theunderlying idea can be summarized by saying that all statements andmathematical equations that are true for signal systems are also truefor antenna systems, provided suitable changes are made in the variablesinvolved so that, in essence, time is converted to space. Thus, inparticular, the field-distribution pattern of the energy fed to anantenna is regarded as an input signal fed to a signal transfer system,and the radiation pattern of the antenna is regarded as the outputsignal of the system. The antenna itself then assumes the role of asignal-transfer system, such as a filter, having a certain well-definedtransfer function, which governs the conversion of the input signal intothe output signal.

-It will thus be seen that the great fund of knowledge built up overrecent years in regard to signal-processing systems, becomes availablefor the study and development of antenna systems and, as alreadymentioned above, the present invention constitutes one particular, andimportant, result encountered along this line of investigation.

Referring to the linear array shown in FIG. 1, consider a continuousradiating source corresponding in over-all shape with that of the array,such as a narrow slot-like radiating aperture of the length d. The fielddistribution of such a continuous linear radiator can be shown to berepresentable by a complex function of the form P 1 1 (1) where A(x),the modulus of the complex function, represents the amplitudedistribution of the electric field along the O-X axis, and (x)represents the phase-angle distribution of the electric field along saidaxis.

Further, since it is known from classic signal theory that the frequencyspectrum of a signal and the law of variation of said signal with timeare Fourier transforms of each other, it can be shown that in analogousfashion the radiation pattern of a continuous radiator can berepresented as the Fourier transform 111(1):) of the fielddistributionfunction F(x), where a is the angular coordinate as indicated in thedrawing. In the usual cases, the Fourier transform will be identicallyzero for angles a outside of a certain angular interval (OL1, +a thatis, the source does not radiate any field outside such interval. It willhere be assumed that this condition is fulfilled. Under this condition,the field function can be subjected to a sampling" operation, which isanalogous to the sampling operation described by Shannon in respect totime-limited signals, and sometimes known as Shannons theorem (cf.Information Theory by Stanford Goldman, ch. II, Prentice-Hall Inc., NewYork 1955).

Thus, by applying a sampling operation similar to that taught by Shannonwith reference to time signals, the complex field-distribution functionF(x) given by Equation 1, above, can be broken down into a sum of termsK F sin 0Z1) where k represents an integer, and A the wavelength to beradiated. The factor 2 sin a Further, the field-strength distributionand phase distribution for the respective radiators of the array aretaken in accordance with the terms of the sum 2.

By introducing the radiator spacing a as just defined, Equation 2 can berewritten in homogeneous form sin qrC-i-K) F (K g) With the arrayconstructed as just specified, the overall radiation diagram of thearray is substantially the same as the radiation diagram of theimaginary continuous radiation source, coextensive with the array, inrespect to radiated waves having the prescribed configuration asdescribed by the complex function If the complex distribution functionrepresents an equiamplitude field-distribution pattern,

which is a frequent case in practice, then the term A(x) in Equation 1is a constant and the field-distribution function takes the reduced formF (th it (t) and in Equation 3, the second factor of each term be- Thearray will then be made up of a series of equispaced radiators at thespacing 2 sin (1 each radiator having a field-distribution pattern ofthe where K represents the position of the radiator in the array.Furthermore, the phase displacement between the signals fed to (or from)adjacent radiators of the array is given by the expression It will benoted that the radiation diagram of each radiator is a sectoral diagramlimited to the angular range (1 1)- The teachings of the invention willnow be applied to two special cases. The first case relates to theconstruction of a radiator array usable for large-angle electronicscanning. The array may serve as an antenna array for transmittingplanar waves in controllable directions within a prescribed scanninginterval, and for receiving echo waves from the same directions.

Considering the imaginary continuous slot radiator of length d, it isapparent from elementary geometric considerations that in the case of aplanar wave, radiated by the array in a direction at an angle a to thenormal IZ, the phase distribution of the energy along the slot aperturemust vary linearly with the distance x as counted from the arrayextremity O, in accordance with the equation (2)33 at A A sna Since thewave configuration is in this case equiamplitude, the complex fielddistribution is of the reduced form given as Equation 4 above, i.e.

F =exp sin a} Further the inter-radiator spacing is taken equal to 2 sinor;

as indicated above.

It is important to note that the radiation diagram of such a source, asgiven by the Fourier transform l/(a), is sectionally continuous over thefinite angular interval a +11 and consequently the sampling of the sinor A and since it is seen that sin a sin or;

The phase shifters such as 19, 29, etc. may assume any suitable form. Ifthe desired deflection angle or is constant, then fixed phase shifters,such as suitably predetermined lengths of waveguide, may be used. If onthe other hand the angle a is to be adjustable, such as in the scanningapplication considered above, then adjustable phase shifters are used,conveniently the digitally controlled phase-shift units disclosed in myco-pending application identified above.

In accordance with an essential feature of the invention, describedabove, the radiators 1, 2, 3, must provide a field-strength-distributionpattern (or illumination law) at the fictive, continuous radiatingaperture, represented by the line OX, which is of the form given byEquation 6 above. The individual field patterns for the radiators 1, 2,3, are obtained by assigning the consecutive integral values 0, l, 2, tothe term K in that equation, viz.:

Radiator 1;

It will be apparent that the field-distribution function for all theindividual radiators is the same, being of the general form sin X Xwhere X represents the abscissa as measured along the direction of thefictive radiating aperture, referred to an origin selected at one sideedge of the radiator considered,

and multiplied by the constant coeflicient 1r/ a, i.e.,

Y 'L' A a (90 ka) The individual field-distribution curves are sodisplaced by the constant amount a along the direction of the abscissae,that the distributions relating to adjacent radiators are orthogonallyrelated, that is, the initial point of zero field strength (or node) forone radiator coincides with the initial point of maximum field strength(or peak) for the next radiator. Owing to this orthogonal relationship,there is, essentially, no mutual coupling 8 between consecutiveradiators in the array. In FIG. 2, the field-distribution laws relatingto the first three radiators 1, 2 and 3 have been partially andapproximately represented above the radiators.

Radiators having the desired field-distribution characteristics asspecified by the equations given above can be constructed in variousways, well understood by those skilled in the art. Thus, suitablydisposed arrays of dipoles and reflectors may be used. However, inaccordance with preferred embodiments of the present invention,especially in the s-h-f and the higher u-h-f frequency bands, theradiators of the array are constructed in the form of multimode hornradiators, as disclosed in my copending application.

FIG. 3 illustrates one such form of construction.

The array shown in that figure may be considered as consisting of aseries of juxtaposed dual radiating sections 10, 20, 30, n0, adjacentones of which have common feeder junctions 11, 21, 31, n1. The dualsections 10 and n0 at the respective ends of the array are furtherconnected at their outer sides with impedancematching loads provided bysuitable shorted waveguides and respectively. Each of the dual radiatingsections, such as section 20 for instance, includes a radiating aperture12, 22, 32, 112 each bounded by two parallel separating walls such as 13and 23 which extend generally along the axial mid-planes of the feederjunctions a predetermined distance inward from the plane of theradiating aperture, as shown. Further, each dual radiating section suchas section 20 has a pair of oblique side walls extending from the sidesof the feeder junctions 11, 21 and converging V-wise so as to define twosymmetrical channels, such as 24 and 25, between said sidewalls and theaforementioned separating walls 13 and 23. The channels 24 and 25 bothterminate outwardly at the radiating aperture 22, while being separatedfrom each other over at least part of their length by a centralseparating wall or septum 26.

The operation of a radiator array of this type will be more fullyunderstood by having reference to my earlier application Ser. No.315,949, filed Oct. 14, 1963, now Pat. No. 3,308,469.

For the purposes of the present disclosure, it is sufii cient toindicate that wave energy applied to the feeder junctions 11, 21, 31, isguided by said feeders and then through the channels such as 24 and 25,in the manner indicated by the dotted arrows, the energy from eachfeeder being equally distributed by the corresponding separating wallsuch as 13 or 23 between adjacent dual radiator sections. In each dualradiator section such as 20, the partial energies applied from the twofeeder junctions such as 11 and 21, associated with that section,combine at the radiating aperture such as 22 so as to provide thereat aresultant field which is the vector sum of the fields derived from thetwo associated feeder junctions. By this method of summation, it ispossible to provide at the radiating aperture of each dual radiatingsection any desired pattern of field-amplitude distribution, with a highdegree of approximation. For this reason the portion of each radiatorsection such as 20 comprising the two channels 24 and 25, outwardlybounded by the separating walls 13 and 23, is called a mode-selector ormoder section of the radiator. The moders can operate in either thetransverse electric or the transversemagnetic modes, and in theillustrated embodiment transverse-electric operation is contemplated,with the E vector at the radiating aperture such as 22 extendingperpendicular to the plane of the drawing. As explained more fully inthe above-identified Pat. No. 3,308,469 a mode-selective radiator of thetype just disclosed makes it readily possible to obtain at the radiatingaperture thereof a fielddistribution pattern which closely approachesthe function sin X 9 at any rate as regards the main or central lobe andthe first side lobes of the distribution curve. This is indicated in theupper part of FIG. 3, where the field amplitude distribution associatedwith each dual radiator section is represented above that section as apair of symmetrical curves, one shown in full lines and the otherdotted, which are respectively created by the energy applied to therespective feeders, such as 21 and 31, associated with the dual radiatorsection under consideration. As will be easily understood, the array ofFIG. 3, instead of being regarded as being composed of a series ofjuxtaposed dual radiator sections as disclosed above, may just as wellbe considered as being made up of a series of juxtaposed horn radiatorseach being coaxial with a feeder junction such as 21 and having itsradiating aperture divided by a separating wall such as 23. When thearray is so considered, it will be seen that each elementary hornradiator therein has a field-amplitude-distribution pattern which isrepresented substantially as the central portion (main lobe and part ofeach of the first side lobes) of the curve sin X these distributioncurves overlapping as shown.

It will be understood that the energy fed to each of the feederjunctions 11, 21, 31 of the array in FIG. 3 is applied by way of arelated phase shifter 19, 29, 39,

as described with reference to FIG. 2, these phase shifters introducingprogressive phase shifts such that the phases of the waves applied toadjacent feeder junctions differ by a desired constant angle,corresponding to the desired inclination angle for the plane waveradiated by the array, as earlier described.

As is known, the directional pattern of a linear array can berepresented as a function of the form where A() represents the relativefield strength of the array and is seen to be the product of twofunctions or factors. Function B(0) characterizes any one of theelements of the array and represents the radiation diagram of suchelement, while function (3(0) characterizes the geometry of the arrayand represents the radiation diagram of an array in which the individualradiators are disposed in the same manner as in the array under consideration, but wherein said individual radiators are omnidirectional incharacter. For an array of the type here considered, function C(fi)represents a curve of the form shown in FIG. 4 for a scanning directionaxially of the array, that is, for the case where the plane wavesradiated by the array have zero inclination. When the scanning angle ofsaid plane waves is varied by varying the phase-shift angle between thewave energy fed to adjacent feeder junctions of the array as aboveexplained, the curve C(0) in FIG. 4 is simply shifted by a correspondingamount along the axis of abscissae. It is manifest therefore that if theradiated plane waves are to retain a constant amplitude for all scanningdirections within the scanning range (-o a and to prevent the occurrenceof substantial secondary lobes in the radiation pattern of the arraywithin said scanning range, it is necessary that the function B(0)representing the directional diagram of each elementary radiator shouldbe constant, i.e. each of the radiators must have a sectoral radiationpattern over the range (-0 0 as shown. Such a sectoral pattern,characterizing each of the elementary radiators in an array according tothe invention, means that the elementary radiator must have anillumination law of the form i sin X til 10 dividual radiators in thearrays of the invention, for optimal scanning performance.

A further embodiment of the invention will now be described withreference to FIG. 5, which schematically illustrates the invention asapplied to spherical, rather than plane, radiated waves. The systemshown in FIG. 5 comprises a primary radiator schematically indicated asthe source S, e.g. a horn antenna, and a secondary radiating arraycomprising a series of radiators 1, 2, n, e.g. horn antennas, allpositioned in mutually irradiating relation with the source S. Assumingelectromagnetic energy is fed by conventional feeder means not shown tothe primary antenna S, the latter will radiate spherical waves; it isdesired that the secondary array shall receive the whole of the energycontained in the portion of the spherical wave limited to the angle 2ondefined by the width d of the array without any loss in gain. Ifconversely it is assumed that energy is fed to the secondary radiators1, 2, n of the array and is radiated therefrom towards the primaryradiator S, it is desired that this radiant energy shall convergespherically at the point S as a focus so as to be absorbed wholly by theprimary radiator without any loss (except for inevitable diffractionring effect).

Applying the teachings of the invention to this particular waveconfiguration, we shall first seek to determine the ideal law or patternof phase distribution that should obtain along a fictive continuousradiator coextensive with the secondary array, in order that the desiredcomplete transfer of energy between such continuous radiator and thespherical waves centered at S shall occur. Considering a point A of saidcontinuous radiator, at a distance x from the origin 0 (taken at one endof the array, as shown), the phase angle (x) at the point A clearly is21r/)\ times the propagation distance A M, where M is the point ofabscissa x on the spherical wave (shown in dashed lines), passingthrough 0. From elementary geometric considerations it is readily foundthat where R is the distance from the source S to the array and d thewidth of the array. Hence,

w gs mm (9) Since in this case also an equiamplitude field distributionis clearly involved (the field amplitude is constant throughout thespherical surface of the wave), the complex fielddistribution functioncan be written, from Equation 4, as:

The Fourier transform of this function tl/(u), which represents thedirectional diagram of the fictive continuous radiator coextensive withthe array, is clearly sectionally continuous over the finite interval(-04 01 since such directional diagram is substantially a sector ofangle 21x Hence, Shannons transposed breakdown theorem is legitimatelyapplicable to this case, and the sampling interval will have the valueHence, in accordance with a second one of the three condrtions of theinvention, the spacing of the secondary radiators along the array willbe According to the third of the three inventive conditions,

1 l the field-amplitude distribution of the energy fed to each radiatoris in accordance with the function where k represents the serial numberof the radiator in the array, and a has the value just specified.

Each of the radiators 1, 2, n of the array of FIG. 5 may be constructedas a multi-mode source, in a general manner similar to that shown inFIG. 3. The radiators are fed by way of feeder junctions in which areinterposed suitable phase shifters, adjusted to impart to the feedenergy a phase shift of the value dictated by Equation 9. Thus, thephase shift applied to the kth radiator of the array is seen from thatequation to be It will be noted that in the system of FIG. 5 theindividual radiators of the secondary array receive the spherical wavesradiated by the primary source S under varying incidence angles,decreasing from the center to the periphery of the array. The conditionof the invention regarding the field-strength distribution of the feedenergy to the individual radiators in accordance with a law of the form(sin X )/X, resulting in a substantially sectoral radiation pattern foreach of said radiators as earlier indicated, in this particular caseensures that the peripheral radiators will receive the energy radiatedby the primary source wtihout any reduction in gain as compared to thecentral radiators of the array. Thus the said condition contributes toassure optimal energy transfer to and from the array, in respect to theparticular, here spherical, wave configuration considered.

For clarity of representation, all the arrays of the invention hereindisclosed have been shown as linear or unidimensional arrays, and thedisclosure has for simplicity referred primarily to arrays of this kind.It is immediately evident, however, that the teachings of the in ventionare directly applicable to two-dimensional, or surface, antenna arrays,and in fact the most useful practical embodiments of the invention wouldcomprise arrays of this last-mentioned type. It is to be understood thatin cases where the invention is applied to a twodimensional array, i.e.an array with a plurality of parallel rows of radiators, each of thethree basic teachings of the invention, respectively relating toradiator spacing, field-strength-distribution pattern for each radiator,and phase-distribution pattern along the array, should be appliedseparately to each of two coordinate directions of the array, whichdirections are conveniently taken as mutually orthogonal. Theconstruction of the two-dimensional array will then be completelydetermined.

It will thus be seen that I have provided a wavetransmitting orwave-receiving system with at least one row of equispaced radiatorswhich are so connected to their associated feeding means (e.g.waveguides) that the individual field-strength-distribution pattern ofeach radiator has the form sin X wherein A(K) and (K) are, respectively,an amplitude factor and a phase factor. Each of these factors is afunction, identical for all radiators as shown above, of the integer Kwhich counts the number of radiators from an end of the row; in the caseof a planar wavefront parallel to the array, as discussed in connectionwith FIGS. 1 and 3, both these functions may be constants. The functionX, having the value 12 as given above, goes to 0 for xaK and becomesequal to r for x=a(K]-l). Thus, if we regard the units 1, 2 and 3 ofFIG. 2 as, respectively, radiator No. 0 (K O), radiator No. 1 (K=l) andradiator No. 2 (K Z), we find that X varies linearly from a point P onone side of any radiator to a point P on the opposite side thereof, eachof these points being spaced by a distance a/Z from the radiator axis 2,as specifically shown for radiator 2. The function sin X f( X varies atthe same time from a peak f=l at point P to a node f=0 at point P alonga curve which assumes the value 2/1r at its intersection with axis 2,,i.e. midway along the range P P The cophasal energization of twoconfronting sections of adjoining radiators from a common waveguide,e.g. as illustrated in FIG. 3 for sections 25 and 26 of radiators 22 and32 connected to feeder 21 with phase shifter 29, generates anapproximation of the above function as indicated by the graph of thatfigure.

What is claimed is: 1. A system for radiating electromagnetic waves of aprescribed geometric configuration, comprising:

an array of radiators having radiant apertures equispaced in at leastone row; and wave-feeding means connected to said radiators forimparting to each radiator a coherent radiation pattern substantially ofthe form A(K) exp j( where A is an amplitude factor, is a phase factorand X is a function of distance varying linearly along said row from 0at a first point on one side of the radiator to 1r at a second point onthe opposite side of that radiator, each of said points lying at adistance of substantially a/2 from the radiator axis where a: is thespacing between successive radiators, K being an integer counting thenumber of radiators from one end of said row, the functions A(K) and (K)being the same for all radiators.

2. A system as defined in claim 1 wherein at least one of said factorsin a constant.

3. A system as defined in claim 1 wherein said Wavefeeding meansincludes individual phase shifters for said radiators.

4. A system as defined in claim 3 wherein said phase shifters are set toimpart to successive radiators progressively varying values of (,0separated by substantially the same difference Agb for any twoconsecutive radiators.

5. A system as defined in claim 3 wherein said phase shifters are set toimpart to successive radiators different phase shifts establishing asubstantially spherically curved overall pattern of radiation centeredon a point remote from said row of apertures.

6. A system as defined in claim 3 wherein said phase shifters areadjustable.

7. A system as defined in claim 1 wherein said radiators are eachdivided into two sections lying on opposite sides of said axis, saidwave-feeding means being co phasally connected to confronting sectionsof any two adjoining radiators.

8. A system for radiating electromagnetic waves of a prescribedgeometric configuration, comprising:

an array of radiators having radiant apertures equispaced in at leastone row, each of said radiators being divided into two symmetricalsections lying on opposite sides of an axis bisecting its aperture alongsaid row; and

wave-feeding means connected to said radiators for imparting to eachradiator a coherent radiation pattern varying along said row from a peakon one side of said axis to a node on the opposite side with anamplitude and a phase respectively determined by a factor A(K) and afactor (K), said but variable phase differences between successive pairswave-feeding means including a plurality of feeders of radiators.

each cophasally connected to a pair of confronting References Citedsections of two adjoining radiators, K being an in- UNITED STATESPATENTS teger counting the number of radiators from one end of said row,the functions A(K) and (K) being 5 2'286'839 6/1942 Schelkunoff 343 8533,205,501 9/1965 Kuhn 343778 the Same all radlamrs' 3 259 902 7/1966Malech 343 777 9. A system as defined 1n claim 8 whereln said feeders3308; 3/1967 343 854 are provided with individual phase shifters forvarying the relative phasing of radiated Wave energy from one 10 ELILIEBERMAN Primary Examiner radiator to the other.

10. A system as defined in claim 9 wherein said phase US. Cl. X.R.shifters are adjustable to provide substantially identical 343786, 854

